Yes, it will just take some time by yourself. You accrue trainer points for pretty much everything from teaching tricks to winning competitions to walking your dog. It takes 2000 trainer points to unlock the first breed, which took me about a week to build up. After that, you unlock a new breed or house design every 2000 points for a while, and then eventually you'll need to accrue tons of points to get the last few things. Also, you don't get to choose what's unlocked. It just goes in order.